Question

Consider a portfolio that is 60% (w_S) in the S&P 500 index and 40% (w_B) in the JPM bond index.

Suppose an analyst estimates that E[r_S] = 15%, σ_s = 20%, E[r_B] = 10%, σ_B =12%, and ρ = 0%.

1) Calculate the portfolio's standard deviation given that the correlation is zero:

2) Calculate the weighted average of the standard deviations of the S&P 500 index and the JPM bond index:

Answer 1

1]

standard deviation for a two-asset portfolio σ_p = (w₁²σ₁² + w₂²σ₂² + 2w₁w₂Cov_1,2)^1/2

w₁ = weight of Asset 1

w₂ = weight of Asset 2

σ₁² = variance of Asset 1

σ₂² = variance of Asset 2

Cov_1,2 = covariance of returns between Asset 1 and Asset 2

Cov_1,2 = ρ_1,2 * σ₁ * σ_2, where ρ_1,2 = correlation of returns between Asset 1 and Asset 2

standard deviation = ((0.60)²(0.20)² + (0.40)²(0.12)² + (2)(0.60)(0.40)(0)(0.20)(0.12))^1/2

standard deviation = 12.92%

2]

weighted average of the standard deviations = (0.60 * 0.20) + (0.40 * 0.12) = 16.80%